Ice sheets form from snow which has been compacted into ice over many years. As snow transitions into ice, it passes through an intermediate stage known as firn. Both the Greenland and Antarctic ice sheets are covered by a firn layer that can be up to ~150 m thick, with lighter firn closer to the surface and denser firn at depth. Firn models aim at representing densification processes as a function of climate (e.g. snowfall and temperature), and model simulations can be performed on large spatial scales, e.g. for ice sheet mass balance assessments, or at individual locations, e.g. for analyses of ice cores. Firn densification models are empirical models, thus relying on calibration with observational data. In this context, there are several sources of inter-model discrepancies: calibration methodology, calibration data, level of model complexity, physical processes included and their parameterisation, and climatic input forcing. For all these reasons, uncertainty about firn densification results is large, yet difficult to evaluate. This thesis aims to better quantify uncertainty from these aspects, and their impact on firn model output.

In Chapter 1, a new model implementation for simulating meltwater percolation in firn models is presented and evaluated. Representing meltwater infiltration and the subsequent effects on firn densification and temperature properties remains a primary source of uncertainty in firn models. This study provides a novel and physics-based approach to represent the meltwater flow process and its interplay with firn densification.

Uncertainty associated with model parameterisation and with the calibration process is addressed in Chapter 2. Using a large dataset of firn cores, a Bayesian calibration framework is designed and used in order to re-estimate model parameter values. This statistical approach further allows to quantify parametric uncertainties and their direct impact on modelled densification rates.

Chapter 3 is the first study to thoroughly evaluate uncertainty in firn thickness changes at the ice sheet scale, the East Antarctic ice sheet more specifically. Using statistical emulation of firn densification models, a large ensemble of model simulations that accounts for the different uncertainty sources in
firn model simulations is constructed. Statistical analysis of the results evaluates spatial patterns of the resulting total uncertainty and quantifies the contributions of the different uncertainty sources. Finally, this study demonstrates the direct impact of such firn model uncertainties on the interpretation of altimetry-based mass balance assessment in East Antarctica.

Together, these chapters bring novel firn physics, statistical techniques, and uncertainty evaluation methods into firn modelling. They contribute to firn model accuracy and robust estimation of uncertainties, both being crucial to several important glaciological applications.